@Riley_S 

The satellite units won't stay on-line for more than minutes at a time. I've done many tests and moves where nothing else on the circuit would be changing. There aren't any devices on the circuit that should have that kind of effect, and none that would be turning on and off at that rate.

The whole house was refurbished less than 10 years ago with new electrical wiring installed. I wouldn't expect any huge degradation in lines in that time frame.

I've moved the satellites between different plugs and the problem persists. The main can only move between a couple of outlets because it has to remain near the router/signal wires, which can't be moved. I hadn't changed that before since it was the only stable part of the network. Based on your response I tried moving that to the only other possible plug and it made no difference.

This particular set of 3 Deco P9s was specfically chosen as it's labeled to support coveage through thick walls (due to the powerline) and have total network coverage up to 6,000 sq ft/560 sq met. I need less than that, but using the satellites on different floors than the main is the point of how the system is to be used. The wifi signal of the existing router with the very thick old walls is typically too weak to be used in the areas where the satellites are being set up. (That's why those areas were chosen.)

I'm happy to try to configure the Deco P9s to not use the powerline feature to see if they're stable with wifi only, but it's not clear to me how to set them up that way (in the Deco App). Any advice/instructions how to do that?

  @JR-IT IMHO

My guess what is happening is unfortunately due to the AC outlet where your main Deco is located is on the other side of the electric breaker panel. The AC power circuits coming in have one neutral and two hots. One Hot goes to the left side of the panel and the other goes to the right side of the panel. 

The Deco P(PowerLine) models use the older original type of PowerLine connectivity, which is incapable of stably or many times even impossible, to connect to circuits across the Electrical Panel from side to side. 

You can test if that is what is happening by choosing only outlets, that are on breakers, on the same side of the Electric Panel, as your Main Deco. If this allows the Satellites to stay stably connected. you can request your Electrician to move the two non functioning outlets over to breakers on the same side as the main Deco. 

Alternatively ... you can try to employ the latest generation of PowerLine devices. They can be identified by their use of the "G.hn" label in their model name or specs. This latest generation of PowerLine is able to transmit across both Hot and Neutral, allowing some connectivity across the breaker panel.

If after testing, the "G.hn" devices work for you at your original electric outlet locations,  then you will need one PowerLine G.hn" at the main deco and another one at each satellite Deco. If you get the AC outlet pass through "G.hn" PowerLine devices, you can maintain using one electric outlet for both PowerLine and Deco Power.

However if this works, then this will effectively supplant your Deco Native PowerLine functions.

So if they are still under a replacement option and the "G.hn" works, replace the Decos and get a non-PowerLine Deco option. 

  @Riley_S 

In the locations I'd like to put the satellites (so the 3 units can cover the important parts of the house) they can connect intermittently with wifi-only but not get consistent connections. This is likely consistent with the fact that I can plug in the units and get a white light and connectivity for a while, but after some number of minutes I get the flashing red light.

I moved the combinations of plugs around some more and I did find a more stable connection with the powerline than I had at first. Between that and perhaps intermittent wifi connection the units seem to be more stable. Or if they're dropping periodically (which I expect maybe they are) perhaps they're recovering more gracefully between a mostly working powerline network and an intermittently working wifi network.

I expect your idea to set up an intermediate location would improve things, but then the set of 3 wouldn't cover the most needed areas. Perhaps I have to get additional nodes to cover the desired area.

Appreciate the suggestions.